Four-manifolds with 1/4-pinched Flag Curvatures

Andrews, B.; Nguyen, Huy T.

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Four-manifolds with 1/4-pinched Flag Curvatures

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Nguyen, Huy T.
Geometric Analysis and Gravitation, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Andrews, B., & Nguyen, H. T. (2009). Four-manifolds with 1/4-pinched Flag Curvatures. Asian Journal of Mathematics, 13(2), 251-270.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-6465-D

Abstract

The Ricci flow on a compact four-manifold preserves the condition of pointwise 1/4- pinching of flag curvatures. Any compact Riemannian four-manifold with 1/4-pinched flag curvatures is either isometric to $\Bbb C\Bbb P^{2}$ or diffeomorphic to a space-form.